Chemistry at the Dirac Point: Diels–Alder Reactivity of Graphene
Most of the interesting physics of graphene results from the singular electronic band structure at the so-called Dirac point, where the conduction and valence bands cross in momentum space. Although graphene is very stable thermodynamically, the electronic structure at the Dirac point facilitates basal plane chemistry including pericyclic reactions such as the Diels–Alder reaction.
We have discovered a series of facile Diels–Alder reactions in which graphene can function either as a diene when paired with tetracyanoethylene and maleic anhydride or as a dienophile when paired with 2,3-dimethoxybutadiene and 9-methylanthracene. In this Account, we seek to rationalize these findings using simple arguments based on considerations of orbital symmetry and the frontier molecular orbital theory.
The graphene conduction and valence bands (HOMO and LUMO) cross at the Dirac point, which defines the work function (W = 4.6 eV). Thus, the HOMO and LUMO form a degenerate pair of orbitals at this point in momentum space with the same ionization potential (IP) and electron affinity (EA). Based on the importance of the energies of the HOMO (-IP) and LUMO (-EA) in frontier molecular orbital (FMO) theory, graphene should be a reactive partner in Diels–Alder reactions due to the very high-lying HOMO and low-lying LUMO (energies of −4.6 eV). Inspection of the orbital symmetries of the degenerate pair of half-occupied band orbitals at the Dirac point confirms that with the appropriate orbital occupancies, both diene and dienophile reaction partners should undergo concerted Diels–Alder reactions with graphene that are allowed based on the Woodward–Hoffmann principles of orbital symmetry.